Load Frequency Control of Multi-Area Power System

Transcription

1 Yurmouk University Al Hijjawi Faculty for Engineering Technology Electrical Power Engineering Department Secondary project: Load Frequency Control of Multi-Area Power System Done by: Hasan Abu Alasal ( ) Mohammed Abu Alhaija ( ) Supervised by: Dr. Muwaffaq Alomoush

2 CONTENTS Page Dedication 3 Abbreviations..4 Summary CHAPTER ONE: REVIEW OF CONTROL SYSTEMS. Introduction to Control Systems...8. Stability The Routh-Hurwitz stability criterion The Root-locus method The PID Controllers.3.. Introduction Basic Operational Amplifier (Op-Amp) Circuit Proportional (P) controller Proportional-Integral (PI) Controller Proportional-Derivative (PD) Controller Proportional-Integral-Derivative (PID) Controller.. 9 CHAPTER TWO: INTRODUCTION TO MATLAB AND SIMULINK. MATLAB SIMULINK CHAPTER THREE: LOAD FREQUENCY CONTROL 3. Frequency-power characteristics of synchronous generators Basic generator control loops The procedure of Load Frequency Control Models and block diagrams Generator Model Load Model Prime Mover Model Governor Model Automatic generation control AGC in single area system AGC in multi-area system Tie-Line Bias Control AGC with Optimal Dispatch of Generation 45 Conclusions and further work.46 References 47

3 DEDICATION This project is dedicated with love and respect to our families for the help, love and emotional support they offered us with no hesitation. And also to our beloved college Alhijjawi for engineering technology for the great environment it gave to us and to our friends and future colleagues, with special thanks to our respectful supervisor Dr. Muwaffaq Alomoush who helped us with all he could, and to the rest of our instructors and friends. So, thanks for every one helped finishing this work. 3

4 ABBREVIATIONS: AGC: Automatic Generation Control. : Load Frequency Control. SD: Speed Droop. ACE: Area Control Error. RA: Reset Action. AVR: Automatic Voltage Regulation. EDG: Economic Dispatch of Generation. 4

5 SUMMERY As the demand of electrical power is increasing and becoming a global issue, the need of interconnecting power systems is growing up; this growth represents a great challenge for power engineers, challenges in making power systems reliable, economic and safe for both supplier and customer, these challenges are represented in different sections of power systems from protection coordination to economic dispatch of generation through other many technical and economical problems. An important problem is the Load Frequency Control () which is directly related to such interconnection in power systems. Other problems related to such interconnection like the Automatic Voltage Regulation (AVR) have less intersection in operation with. So, in this project, we will mainly display the causes and effects of the () problem, trying to configure its mechanism and to simulate the system response to such control. As the name (Load Frequency Control) indicates, this topic deals with the control of frequency of the system as the load (demand) varies. Since the frequency of the system does affect the whole operation of the system, especially for interconnected power systems of multi-area, and as the main objective of control in power systems is to generate and deliver power as economically and reliably as possible, then it is important to consider the control of the frequency of the system. Frequency and generation control is the major problem in interconnected power networks. If a network frequency is changed over ±0%, units can leave from synchronization with the network. These changes are to make impossible the network interconnection. This issue is becoming more significant recently with increasing size, changing structure, and complexity of interconnected power systems. So, to provide the stability of a system, active power balance and 5

6 constant frequency are required. Frequency depends on active power balance. If any change occurs in active power demand/generation in power system, frequency can not be held in its rated value. So, oscillations increase in both power and frequency. Thus, system subjects to a serious instability problems. To improve the stability of a power network, it is necessary to design a load frequency control system that controls the power generation and active power of tie lines. In an interconnected power system network with two or more areas, the generation within each area has to be controlled so as to maintain scheduled power interchange. Because of the relationship between active power and frequency, three-levels of automatic generation control have been proposed by power system researchers. Levels of Load Frequency Control has to be of two main control loops, these are primary and secondary control. In primary control, control action is realized by turbinegovernor system in the plant. In this control level only the active power is balanced. However, maintaining the frequency at scheduled value (e.g. 50 Hz) can not be provided. Therefore, steady state frequency error can occur forever. So this level is not enough for interconnected systems, as the frequency must be equal at all areas. The second level of generation control, called secondary or supplementary control is made in large power systems which include two or more areas. Active power is controlled at the tie lines between neighbor areas by the concept of Automatic Generation Control (AGC) and there are central and local load control and distribution centers. The final level of generation control is Economic Dispatch of Generation (EDG) among the all plants. The major aim of this control is to maintain each unit s generation at the most economic value. Among this project we are interested only in the two main control levels, namely the primary and secondary. 6

7 No one of these control levels could be understood or realized with out understanding the main concepts of control system theory, so a review of some important concepts of the control system theory is given in chapter one of this project, farther more, considering the importance of the PID controllers, being the most kwon and popular controllers in control systems, a special section of chapter one was added. Also, as the facility of simulating the response of our systems of interest is the MATLAB program and its SIMULINK package, another chapter (Chapter two) is given as a review of the basics of MATLAB and SIMULINK. Finally, the main chapter of this project; chapter three is concerned with the analysis of the main elements and loops of, and in the simulation of single and interconnected multi-area (two-area) power systems, respectively. 7

8 CHAPTER REVIEW OF CONTROL SYSTEMS. INTRODUCTION TO CONTROL SYSTEMS The first step in the analysis and design of any control system is the mathematical modeling of the system. The two most common methods are the transfer function approach and the state equation approach. The state equations can be applied to portray linear as well as non-linear systems. As all physical systems are non-linear to some extent, then, in order to use the transfer function and linear state equations, the system must first be linearized. Thus, proper assumptions are made so that the system can be characterized by a linear mathematical model [4]. The model may be validated by analyzing its performance for realistic input conditions and then by comparing with field test data taken from the dynamic system in its operating environment. Once an acceptable controller has been designed and tested on the model, the feedback control strategy is then applied to the actual system to be controlled. When we wish to develop a feedback control system for a specific purpose, the general procedure may be summarized as follows:. Choose a way to adjust the variable to be controlled; e.g. the mechanical load will be positioned with an electric motor or the temperature could be controlled by an electrical resistance heater, (or active power generated can be controlled by adjusting the valves of the governor of the turbine).. Select suitable sensors, power supplies, amplifiers, etc.., to complete the loop. 3. Determine what is required for the system to operate with the specified accuracy in steady-state and for the desired response time. 8

9 4. Analyze the resulting system to determine its stability. 5. Modify the system to provide stability and other desired operating conditions by redesigning the amplifier/controller, or by introducing additional control loops [4]. The objective of the control system is to control the output c(t) in some prescribed manner by the input r(t) through the elements of the control system. Some of the essential characteristics of feedback control system are investigated in the following sections.. STABILITY: Considering the block diagram of a simple closed loop control system as shown in Fig. below, where R(s) is the S-domain reference input, C(s) is the S-domain controlled output, G(s) is the plant transfer function, k is a simple gain controlled, and the feedback element H(s) represents the sensor transfer function. The closedloop transfer function is: C ( s) k G ( s) = T ( S ) = (.) R( s) + ( k G ( s) H ( s)) R (s) k G (s) C (s) H (s) Fig... Block diagram of simple closed loop system. or the s-domain response is: C ( s ) = T ( s ) R ( s ) (.) The gain, k G ( s) H ( s), is commonly referred to as the open-loop transfer function. For a system to be usable, it must be stable. A linear time-invariant 9

10 system is stable if every bounded input produces a bounded output. We call this characteristic stability. The denominator polynomial of the closed-loop transfer function set equal to zero is the system characteristic equation. That is the characteristic equation is given by: + k G ( s) H( s) = 0 (.3) The roots of the characteristic equation are known as the poles of the closedloop transfer function. The response is bounded if the poles of closed-loop system are in the left-hand portion of the s-plane. Thus, a necessary and sufficient condition for a feedback system to be stable is that all the poles of the system transfer function have negative real parts. In the classical control theory, several techniques have been developed requiring little computation for stability analysis, one of these techniques is the Routh-Hurwitz criterion. Consideration of the degree of stability of a system often provides valuable information about its behavior. That is, if it is stable, how close it is to being unstable? This is the concept of relative stability. Usually, relative stability is expressed in terms of the speed of response and overshoot. Other methods frequently used for stability studies are the Bode diagram, Root-locus, Nyquist criterion, and Lypunov s stability criterion, but we are to consider Routh- Hurwitz and Root-locus methods here [4].... THE ROUTH-HURWITZ STABILITY CRITERION The Routh-Hurwitz criterion provides a quick method for determining absolute stability that can be applied to an n th order characteristic equation of the from a s a s a s n n = (.4) n n 0 a 0 The criterion is applied through the use of a Routh table defined as: 0

11 s n a n a n a n 4.. s n a n a n 3 a.. n 5 s n b b b 3.. s n 3 c c c a n, a n-,., a 0 are coefficient of the characteristic equation and b a a a a a n n n n 3 = ; n b = a n a n 4 a n a n a n 5 c b a a b b n 3 n = ; c = b a n 3 a b n b 3 Calculations in each row are continued until only zero elements remain. The necessary and sufficient condition that all roots of (.4) lie in the left of the s-plane is that the elements of the first column of the Routh-Hurwitz array have the same sign. If there are changes of signs in the elements of the first column, the number of sign changes indicates the number of roots with positive real parts. If the first element in a row is zero, it is replaced by a very small positive number Є, and the calculation of the array is completed. If all elements in a row are zero, the system has poles on the imaginary axis, pairs of complex conjugate roots forming symmetry about the origin of the s-plane, or pairs of real roots with opposite sings. In this case, an auxiliary equation is formed from the preceding row. The all-zero row is then replaced with coefficients obtained by differentiating the auxiliary equation [4] [7].

12 ... THE ROOT-LOCUS METHOD The Root-locus method, developed by W.R. Evans, enables us to find the closedloop poles from the open-loop poles for all the values of the gain of the open-loop transfer function. The Root-locus of a system is a plot of the roots of the system characteristic equation as the gain factor k is varied. Therefore, the designer can select a suitable gain factor to achieve the desired performance criteria. If the required performance can not be achieved, a controller can be added to the system to alter the root-locus in the required manner. Consider again the feed-back control system given in Fig.. In general, the open loop transfer function is given by: z p k ( s + )( s + )...( s + ) m k G ( s) H( s) = (.5) ( s + )( s + )... ( s + ) Where m is the number of finite zeros, and n is the number of finite poles of the loop transfer function. If n > m, there are ( n m ) zeros at infinity. The characteristic equation of the closed-loop transfer function is given by (.3); therefore ( s + ( s + p z p z z p p z )( s + )....( s + ) n = k (.6) )( s + )......( s + ) From equation.6 it follows that for a point s o in the s-plane to be on the rootlocus, when 0 < k <, it must satisfy the following two conditions. product product of of vector vector lengths lengths from from finite finite o k = (.7) And m z p poles zeros n to s to s o angles of zeros of G H( s) angles of poles of G H( s) = r(80 ) (.8) where r =±, ±3, ±5, A good knowledge of the characteristics of the root-loci offers insights into the effects of adding poles and zeros to the system transfer function. It is important to know how to construct the root-locus by hand, so we can design a simple system and be able to understand and develop the computer-generated loci [4]. o

13 .3 THE PID CONTROLLERS:.3. Introduction: When working with applications where control of the system output due to changes in the reference value or state is needed, implementation of a control algorithm may be necessary. Examples of such applications are motor control, control of temperature, pressure, flow rate, speed, force,, AVR or other variables. The PID controller can be used to control any measurable variable, as long as this variable can be affected by manipulating some other process variables. Many control solutions have been used over the time, but the PID controller has become the industry standard due to its simplicity and good performance. For further information about the PID controller and its applications the reader should consult other sources [3]. In Figure. a schematic of a system with a PID controller is shown. The PID controller compares the measured process value y with a reference set point value, y 0. The difference or error, e, is then processed to calculate a new process input, u. This input will try to adjust the measured process value back to the desired set point. The alternative to a closed loop control scheme such as the PID controller is an open loop controller. Open loop control (no feedback) is in many cases not satisfactory, and is often impossible due to the system properties. By adding feedback from the system output, performance can be improved. y 0 - e PID u SYSTEM y Figure. Closed Loop System with PID controller Unlike simple control algorithms, the PID controller is capable of manipulating the process inputs based on the history and rate of change of the signal. This gives a more accurate and stable control method. The basic idea is that the controller 3

14 reads the system state by a sensor, and then it subtracts the measurement from a desired reference to generate the error value. The error will be managed in three ways, to handle the present, through the proportional term, recover from the past, using the integral term and finally to anticipate the future, through the derivate term. Figure.3 shows the PID controller schematics, where T p, T i and T d denote the time constants of the proportional, integral, and derivative terms respectively [3]. e T P T d d dt + + u + T i Figure.3 The PID controller schematic..3. Basic Operational Amplifier (Op-Amp) Circuit Figure.4 shows a simple Op-Amp circuit with input voltage V i (s), output voltage V o (s), input impedance Z i (s) and feedback impedance Z f (s) [3]. It can be shown that the transfer function of the circuit can be written as Z Z Vo ( s ) ( s ) f G ( s) = = (.9) Vi ( s) ( s) i Z f (s) V i (s) Z i (s) - + V o (s) Figure.4 Operational amplifier (Op-Amp) schematic of PID controller. 4

15 Simple RC circuits can be used to generate the input and feedback impedances required to generate transfer functions for P, PI, PD, and PID controllers. To understand the implementation of the controllers described below, recall: ) The total impedance of two components in series is the sum of the individual impedances; and ) The inverse of the total impedance of two components in parallel is the sum of the inverses of the individual impedances. Note that the impedance of a resistor with resistance R is Z(s) = R, and the impedance of a capacitor of capacitance C is Z(s) =. (.0) The total impedance of a resistor and a capacitor in series is c s R C s + Z(s) = R + = (.) C s C s The inverse of the total impedance of a resistor and capacitor in parallel is = C s Z(s) R + (.) So the total impedance of the two in parallel is R Z(s) =. (.3) R C s Proportional (P) Controller To form a P controller, let the input impedance be generated by a resistor of resistance R i, and let the feedback impedance be generated by a resistor of resistance R f. In this case, the impedances are Z i (s) = R i and Z f (s) = R f, and the transfer function of the circuit is R R f G ( s) = = Kp = constant. (.4) i The proportional term (P) gives a system control input proportional with the error. Using only P control gives a stationary error in all cases except when the system control input is zero and the system process value equals the desired value. 5

16 In Figure.5 the stationary error in the system process value appears after a change in the desired value (ref). Using a too large P term gives an unstable system. Figure.5. Step response of P controller..3.4 Proportional-Integral (PI) Controller To form a PI controller, let the input impedance be generated by a resistor of resistance R i and a capacitor of capacitance C i in parallel, and let the feedback impedance be generated by a capacitor of capacitance C f. In this case, the impedances are z i R Rici And the transfer function of the circuit is: i = and z =. (.5) f + s c f R C C s + i i i Ki G ( s) = = + = Kp + (.6) s C R S C R C s f i f i f 6

17 The integral term (I) gives an addition from the sum of the previous errors to the system control input. The summing of the error will continue until the system process value equals the desired value and these results in no stationary error when the reference is stable [3]. The most common use of the I term is normally together with the P term, called a PI controller. Using only the I term gives slow response and often an oscillating system. Figure.6 shows the step responses to an I and PI controller. As seen, the PI controller response have no stationary error and the I controller response is very slow. Figure.6. Step response of I and PI controller Proportional-Derivative (PD) Controller To form a PD controller, let the input impedance be generated by a resistor of resistance Ri and a capacitor of capacitance Ci in parallel, and let the feedback impedance be generated by a resistor of resistance R f. In this case, the impedances Ri are: Z i = ; and Z f =R f And the transfer function of the circuit is Ri Ci s + 7

18 R C R [ s] s + i i f G (s) = R = R C s = i + f i k + p k (.7) d R i R i The derivative term (D) gives an addition from the rate of change in the error to the system control input. A rapid change in the error will give an addition to the system control input. This improves the response to a sudden change in the system state or reference value. The D term is typically used with the P or PI as a PD or PID controller. A too large D term usually gives an unstable system. Figure.7 shows D and PD controller responses. The response of the PD controller gives a faster rising system process value than the P controller. Note that the D term essentially behaves as a highpass filter on the error signal and thus easily introduces instability in a system and make it more sensitive to noise. Figure.7 Step response of D and PD controller. 8

19 .3.6. Proportional-Integral-Derivative (PID) Controller To form a PID controller with high frequency gain limit, let the input impedance be generated by a resistor (resistance, R ) be in series with a resistor (resistance, R ) and a capacitor (capacitance C ) that are in parallel, and let the feedback impedance be generated by a resistor (resistance, R f ) and a capacitor (capacitance C f ) in series. In this case, the impedances are R Z = i R R C s + and R s f C f + Z f s C f Then, it can be shown that the transfer function of the circuit is R C R C R C + = (.8) + f f f i G ( s) = + + s = + + s (.9) + + s + k p s k d ( R R ) C ( f R R ) C ( f R R ) R k Using all the terms together, as a PID controller usually gives the best performance. Figure.8 compares the P, PI, and PID controllers. PI improves the P by removing the stationary error, and the PID improves the PI by faster response and no overshoot [3]. Figure.8 Step response P, PI and PID controller. 9

20 CHAPTER INTRODUCTION TO MATLAB AND SIMULINK. MATLAB MATLAB developed by Math works Inc. is a software package for high performance numerical computation and visualization. The combination of analysis capabilities; flexibility, reliability, and power full graphics makes MATLAB the premier software package for electrical engineers. MATLAB provides an interactive environment with hundreds of reliable and accurate built-in mathematical functions. These functions provide solutions to a broad range of mathematical problems [5]. The most important feature of MATLAB is its programming capability which is very easy to learn and use, and which allows user-development functions. There are several optional toolboxes written for special applications such as signal processing, control systems design, system identification, and others. MATLAB has been enhanced by the very powerful SIMULINK program. SIMULINK program is a graphical mouse-driven program for the simulation of dynamic systems. SIMULINK enables students to simulate linear, as well as nonlinear, systems easily and efficiently [4] [5]... SIMULINK SIMULINK is an interactive environment for modelling, analyzing and simulating a wide variety of dynamic systems. SIMULINK provides a graphical user interface for constructing block diagram models using "drag-and-drop" operations. 0

21 A system is configured in terms of block diagram representation from a library of standard components. It is very easy to learn, a system in block diagram representation is built easily and the simulation results are displayed quickly. Simulation algorithms and parameters can be changed in the middle of a simulation with intuitive results, thus providing the user with a ready access learning tools for simulating many of the operational problems found in the real world [5]. SIMULINK is particularly useful for studying the effects of nonlinearities on the behaviour of the system. It is also an ideal research tool, the key features of SIMULINK are: - Interactive simulations with live display. - A comprehensive block library for creating linear, nonlinear, discrete or hybrid multi-input/output systems. - Seven integration methods for fixed step, variable step, and stiff systems. - Mask facility for creating custom blocks and block libraries. Simulation parameters and solvers We can set the simulation parameters and select the solver by choosing parameters from the simulation menu. The simulation parameters dialog box, have three pages: solver, workspace I/O and diagnostic. The solver page allows us to: Set the start and stop points. Choose the solver and specify solver parameters. Some solvers may be more efficient than others at solving particular problems. There are variable step and fixed step solvers:

22 Variable step solver: can modify their step sizes during simulation. These are ode45, ode3, ode3, ode55, ode3s and discrete. Fixed step solver include ode5, ode4, ode3, ode, ode and discrete. Block diagram construction The SIMULINK BLOCK LIBRARY contains seven icons; each icon contains various components in the titled category. The easy to use pull down menus allows you to create a SIMULINK block diagram, or open an existing file, perform the simulation and make any modifications. Generally, when building a model, design it first on paper, and then build it using the computer. When you start putting the blocks together into a model, add the blocks to model window, before adding the lines that connect them. This way, you can reduce how often you need to open block libraries [5].

23 CHAPTER 3 LOAD FREQUENCY CONTROL 3. FREQUENCIES-POWER CHARACTERISTICS OF SYNCHRONOUS GENERATOR Since synchronous generators are the most common type of machines used in the generation of electrical power, its characteristics can be used to describe the relationship between frequency and power during load changes []. All generators are driven by a prime mover, which is the generators source of mechanical power. The most common type of prime mover is a steam turbine, but other types include diesel engines, gas turbines, water turbines, and even wind turbines. Regardless of the original power source, all prime movers tend to behave in a similar fashion as the power drawn from them increases, the speed at which they turn decreases. The decrease in speed is in general non-linear, but some form of governor mechanism is usually included to make the decrease in speed linear with an increase in power demand. Whatever mechanism is presented on a prime mover, it will always be adjusted to provide a slight drooping characteristic with increasing load. The Speed Droop (SD) of a prime mover is defined by the equation n n n fl nl fl SD = 00% (3.) Where n nl is the no-load prime-mover speed and n fl is the full-load prime-mover speed. Most generator prime movers have a speed droop of to 4 percent, as defined in equation 3

24 (3.). In addition, most governors have some type of set point adjustment to allow the noload speed of the turbine to be varied. A typical speed-versus-power plot (known as the house curve) is shown in figure (3..a). Mechanical speed, rpm n nl n fl Frequency, Hz 0 P fl Power 0 P fl Power kw kw (a) f nl f fl (b) Figure 3. Speed-power and frequency-power curves (house curves). Although the house curves are only used for studying the parallel operation of two generators or that of a single generator connected to a certain network, it helps understanding the variations of electrical frequency as the power demanded is changed, since the shaft speed is related to the resulting electrical frequency by the equation, f n = (3.) e 0 Then the power output of a synchronous generator is related to its frequency and this is clear in figure (3..b). Frequency-power characteristics of this sort play an essential role in the parallel operation of synchronous generators. The relationship between frequency and power can be described quantitatively by the equation P = (3.3) s P where P = power output of the generator f nl = no-load frequency of the generator f sys = operating frequency of system s p = slope of curve, in kw/hz or MW/ Hz. 4 m p ( ) f nl f sys

25 But this equation is not accurate for multi-area power systems. A similar relationship can be derived for the reactive power Q and terminal voltage V T, for which the AVR control loop is used, which is not of our interest in this project []. 3. BASIC GENERATOR CONTROL LOOPS As real power affects the frequency of a network, whereas no big change in the reactive power due to change in frequency, since reactive power is mainly dependent on voltage magnitude (: controls frequency and real power, AVR: controls voltage magnitude and reactive power). Each of them can be controlled separately and independently []. and AVR for generator are shown in the schematic diagram of Fig 3.. Excitation System Gen. Field Automatic Voltage Regulator (AVR) Voltage Sensor Steam Turbine G P V P G, Q G Valve Control Mechanism P tie P C Load Frequency Control () Frequency sensor Figure 3. and AVR of a synchronous generator. The controllers are set to take care of any changes in load demand to maintain the frequency and voltage within specified limits. Small changes in real power refer to change in the angle δ (rotor angle) and this will affect the frequency. 5

26 Since reactive power depends on V, thus the excitation of the generator is a factor affects reactive power. There is a time constant for each of the prime mover and the generator excitation, and this time is much smaller for prime mover and its transient decay becomes faster. For this reason, the load frequency and voltage excitation are analyzed and controlled separately and independently. 3.3 THE PROCEDURE OF LOAD FREQUENCY CONTROL () There are three operation objectives for : - To maintain reasonably uniform frequency. 3- To control tie-line interchange schedules. - To divide the load between the generators. Changes in frequency and real power are sensed, and these are a measure of changes in rotor angle (δ); so the error δ is to be corrected. Error signals such as f and P are amplified, then mixed, then transformed into a real power signal, which is sent to turbine to cause an increment in torque. Therefore, the prime mover (steam turbine) cause changes in the generator output by certain amount to change the value of f and P within a specified tolerance, this mechanism is discussed in details when we consider the modeling of governor and prime mover. Typical responses to real power changes are illustrated using the simulation techniques available in the SIMULINK package of the MATLAB program, these responses will be viewed for each specified control loop. As illustrated in chapter one there are two common methods for modeling, the transfer function method, and this is used for linear systems only where as; the state variable approach, is used in linear and non-linear systems. If we want to use transfer function method; non-linear systems must be linearized. 6

27 3.4 MODELS AND BLOCK DIAGRAMS Generator Model: We have the equation (the swing equation of synchronous machine) Ω ( s) = [ Pm ( s) Pe ( s)] (3.) H s Where the input is P m (the mechanical input power), and the output is Ω (frequency deviation) and P e is the electrical power and H is the per unit inertia constant having a unit of seconds and ranging from to 0 seconds depending on the type and size of the machine [] [6]. The block diagram is as shown in figure 3.3: P m (s) H s Ω(s) P e (s) Figure 3.3 Generator block diagram Load Model: In power systems, the loads are mainly resistive loads, and this is independent of frequency. And the other type of loads is Motor loads (mainly inductive), which is sensitive to change in frequency, depending on the composite of the speed-load characteristic of all driven devices. Speed load characteristic of composite load is: Pe = PL + D ω (3.) Where; P L : independent frequency loads. D ω: frequency sensitive loads. D: ratio of percent change in load to percent change in frequency. And the block diagram of the load model added to that of generator is shown in Figure 3.4: 7

28 P L (s) P m (s) Hs + D Ω(s) Figure 3.4 Load block diagram Prime Mover Model: It is the source of mechanical power; it may be a hydraulic turbine at waterfalls, steam turbine whose energy comes from burning of gas, coal, and gas turbine. Its model relates changes in mechanical power out put P m to changes in steam valve position P V, then Pm ( s) GT ( s) = = (3.3) P ( s) +τ ( s) V which have a single time constant τ T, and its block diagram is shown in figure 3.5: T P V (s) Figure 3.5 Prime mover block diagram. + τ T s P m (s) The time constant τ T varies from 0. to ms Governor Model: The governor is a device used to sense a turbine speed changes when the load of the generator is suddenly increased, in that case, the electrical power exceeds the input mechanical power. The shortage of this power is supplied by kinetic energy stored in the rotating system, reducing the mechanical power of the turbine, [7] [8]. This reduction in energy causes the turbine speed to fall and thus the generator frequency to fall. Any change in speed is sensed by the turbine governor, which will act to adjust the input valves of the turbine to change the output mechanical power to bring the speed to a new steady state. There are many types of governors; 8

29 the earlier types used mechanical mechanisms of sensing speed changes, and modern governors use electronics. Figure 3.6 shows a schematic for a conventional governing system. Lower M Raise Speed changer Hydraulic amplifier To governorcontrolled valves To close To open Speed Governor Figure 3.6 A schematic of a governing system. The speed governor acts as a comparator whose output P g is the difference between the reference set power P ref and the power ω, that is R P g = P ref ω (3.4) R In the s-domain: Pg ( s) = Pref ( s) Ω( s) (3.5) R where R is the speed regulation. Governors typically have speed regulation of 5 to 6 percent from zero to full load. Consider a simple time constant τ g and assume linear relationship, we have the relation: PV ( s) = Pg ( s) + τ s The block diagram is as shown in figure 3.7: g (3.6) 9

30 P ref (s) P g + τ g ( s ) P V (s) ω(s) R Figure 3.7 Governor Block diagram Combining block diagrams of the preceding models we can find the block diagram of the of an isolated power station, providing the primary level of as shown in Figure 3.8. P ref (s) P g + τ g s P v +τ T s P L (s) P m Hs+D Governor Turbine Rotating mass and load Ω(s) R Figure 3.8 block diagram of an isolated power system. For the purposes of simulation, predetermined parameters are given as: Turbine time constant τ T = 0.5 sec. Governor time constant τ g = 0. sec. Governor inertia constant H = 5.0 sec. Governor speed regulation R = 0.05 per unit, and a sudden load change of 0. per unit is represented by a step input at P L and the load is considered to vary by 0.8 percent for a percent change in frequency, i.e., D = 0.8. The block diagram constructed using Simulink is shown if figure 3.9 followed by the response of the simulation in figure (3.0) with the suggested values of time constants and other parameters []. 30

31 Figure 3.9 Simulink block diagram of isolated power system Frequency [pu] Time [sec] Figure 3.0 simulation results of figure 3.9. With the load change - P L (s) as an input, and the frequency deviation Ω(s) as an output, results the block diagram in figure 3. - P L (s) Hs + D Ω(s) R( +τ s)( + τ s) g T Figure 3. with input - P L (s) and output Ω(s) The open loop transfer function is: K G ( s) H( s) = (3.7) R (H s + D)( +τ s)( + s) g τ T And the closed loop transfer function is: 3

32 Ω( s) P ( s) L ( + τ gs)( + τ T s) = (Hs + D)( + τ s)( + τ s) + / R g T = T ( s) (3.8) Or: Ω ( s) = P ( s) T ( s) (3.9) L PL The load change in a step input (i.e. PL ( s) = ) then the steady-state value of s ω is: ω ss = lims Ω( s) = PL (3.0) s 0 ( D + / R) We can find that for the case of no frequency sensitive load (i.e. with D=0) then the steady-state value of the frequency deviation is: ω = ( R (3.) ss P L ) If we have a case of multiple generators with governor speed regulations, R, R,.R n then: ω ss = PL (3.) ( D + / R + / R / R ) n 3.5 AUTOMATIC GENERATION CONTROL (AGC) When the load on the system is increased, the turbine speed drops before the governor can adjust the input of the steam to the new load. As the change in the value of speed diminishes, the error signal becomes smaller and the position of the governor fly-balls gets closer to the point required to maintain a constant speed. However, the new constant speed will not be the set point, and there will be an offset. One way to restore the speed or frequency to its nominal value is to add an integrator; Because of its ability to return a system to its set point, integral action is also known as the reset action. Thus, as the system load changes continuously, the generation is adjusted automatically to restore the frequency to its nominal value. This is known as the Automatic Generation Control (AGC). The role of AGC is to divide the load among system stations and generators to achieve 3

33 maximum economy and to correctly control the scheduled interchanges of power, while maintaining reasonable uniform frequency [], [7], [8] AGC in single area system In order to reduce frequency deviation to zero, we must provide a reset action; the reset action can be achieved by adding integral controller. The system with addition of integral controller is shown in figure 3.. P ref (s) + ( s) + ( s) H s + D τ g P V τ T P L (s) P m Governor Turbine Rotating mass and load ω(s) R K I s Figure 3. AGC for an isolated power system. For the same single area system given before with the same values of τ T, τ g, H, D and P L, with the gain of the I controller suggested to be K I = 7.0. The Simulink diagram constructed is shown in figure 3.3 followed by its response shown in figure 3.4 []. Figure 3.3 Simulink block diagram of isolated power system with AGC loop. 33

34 4 x Frequency [pu] Time [sec] Figure 3.4 Simulation results of figure 3.. Combining the parallel branches results in the following block diagram in fig 3.5: - P L (s) Hs + D ω(s) K I ( + )( )( ) s R +τ s +τ s g T Fig 3.5. Equivalent of AGC of isolated power station. The transfer function is: Ω( s) s( + τ gs)( + τt s) = P ( s) s(hs + D)( + τ s)( + τ s) + K + s L g T I / R (3.3) 34

35 3.5.. AGC in multi-area system: The AGC of multi-area system can be realized by studying first the AGC for a two-area system. Look at figure 3.7. P X Area Area Figure 3.6 Schematic of two-area system. Consider these two areas represented by an equivalent generating units interconnected by a lossless tie line with reactance X tie []. Each area is represented by voltage source behind an equivalent reactance as shown in figure 3.7. X X tie X + - E δ E δ + - Figure 3.7 The equivalent network of two area system. During normal operation the real power transferred over the tie line is given by: E E P = (3.4) sinδ X Where: X = X + X tie + X and δ = δ δ Equation 3.4 can be linearized for a small deviation in the flow P from the nominal value, that is: 35

36 dp P = δ δ = δ 0 dδ s P (3.5) P s : the slope of the power angle curve at the initial operating angleδ = δ 0 δ 0, 0 thus: dp E E P s = δ = cos δ (3.6) dδ 0 0 X Then P = P ( δ ) (3.7) s δ The direction of the flow depends on the phase angle difference; if δ >δ the power flows from area to area. A block diagram for the two area system is shown below in Fig 3.8. R P L (s) P ref (s) P V + τ + τ s gs T P m H s+ D ω (s) Governor Turbine Rotating mass and load + P P s s + P ref (s) P V + τ g s + τ T s Governor Turbine P m P L (s) H s+ D Rotating mass and load ω (s) R Figure 3.8 Two area system with only primary loop (AGC). 36

37 Again, for the purposes of simulation, a two-area system connected by a tie line is suggested to have the following parameters on a 000 MVA common base. Area Speed Regulation R = 0.05 R = Frequency-sens. load coeff. D = 0.6 D = 0.9 Inertia constant H = 5 H = 4 Base power 000 MVA 000 MVA Governor time constant τ g = 0. sec τ g = 0.3 sec Turbine time constant τ T = 0.5 sec τ T = 0.6 sec The Simulink block diagram for such system is shown in figure 3.9, followed by the resulting response in figure 3.0. Figure 3.9 Simulink block diagram of tow area system with AGC loop. 37

38 Figure 3.0 (a) Frequency deviation 0.35 Delta P m 0.3 Delta P m Delta P Power [pu] Time [sec] Figure 3.0 The resulting response of figure 3.9. Figure 3.0 (b) Power deviations 38

39 Consider load change in area is P L, in the steady-state; both areas will have the same steady-state frequency deviation; ω = ω = ω Now, P ω and + P = ω D (3.8) m P PL = D P m The change in mechanical power is determined by the governor speed characteristic, given by: Solving for ω: ω ω Pm = and Pm = (3.9) R R ω = L : + D ) +P ( + D ) R R ( P L = (3.0) B + B Giving B = + R D and, B = + R D where B and B are known as the frequency bias factors. The change in the tieline power is: ( + D ) PL R B P = = ( P L ) (3.) ( + D ) + ( + D ) B + B R R We can easily extend the tie-line bias control to an n-area system. 39

40 3.5.3 Tie-Line Bias Control Up to now, was equipped with only the primary control loop, a change of power in area was met by the increase in generation in both areas associated with a change in the tie-line power, and a reduction in frequency. In the normal operating state, the power system is operated so that the demands of areas are satisfied at the normal frequency [] [7] [8]. As mentioned in section 3.3, a simple control strategy for the normal mode is: Hz). To Keep frequency approximately at the nominal value (50 or 60 schedule. To Maintain the tie-line flow at about changes. Each area should absorb its own load Conventional is based upon tie-line bias control, where each area tends to reduce the Area Control Error (ACE) to zero. The control error for each area consists of a linear combination of frequency and tie-line error. ACE i = n j = P i j + K i ω (3.) The area bias K i determines the amount of interaction during a disturbance in the neighboring areas. An overall satisfactory performance is achieved when K i is selected equal to the frequency bias factor of that area, i.e. B R i + Thus, the ACEs for a two-area system are i D = (3.3) i ω ω ACE = + P B (3.4) ACE = P where P and P are departures from scheduled interchanges. ACEs are used as actuating signals to achieve changes in the reference power set points, and when steady-state is reached, P and ω will be zero. The block diagram of a simple AGC for a two-area system with ACE loops is shown in figure (3.). + B 40

41 B R P L (s) ACE K I s P V + τ g s + τ T s P m H s + D Governor Turbine Rotating mass Go and load ω (s) + P P P s s + + ACE K I s P V + τ g s + τ T s Governor Turbine P m Go H s + D Rotating mass and load ω (s) R P L (s) B Figure 3. A simple AGC for a two-area system with ACE loops. Here the same data is considered for the two area system, except the addition of the ACE loops, adjusting the integrator gain constants for a satisfactory response; the simulation results for K I = K I = 0.3 were obtained. Other than trail and error technique, there is no certain method that suggests an optimal evaluation for the gains of the PID controllers used in such control except using new optimization techniques or artificial intelligence techniques such as fuzzy logic or artificial intelligence, which are all beyond the scope of this project. In this project we used the method of trial and error such that an optimal response was achieved according to the characteristics of optimal step response of control systems. The Simulink block diagram of two area power system with both AGC and ACE loops is shown in figure 3. followed by the resulting response of this simulation shown in figure

42 Figure 3. Simulink block diagram of two area system with both AGC and ACE loops. 4 x 0-3 Delta w Delta w 0 - Frequency [pu] Time [sec] Figure 3.3 (a) Frequency deviation 4

43 Delta P m 0.3 Delta P m Delta P Power [pu] Time [sec] Figure 3.3 The resulting response of figure 3.. Figure 3.3 (b) Power deviation. For a better and more satisfactory response, the I term used in figure 3. for the ACE is replaced by a full PID controller in figure 3.4 followed by its response in figure 3.5 for both frequency and power deviations. Figure 3.4 Simulink block diagram of two area system with both AGC and ACE loops with full PID controller used instead of the I term only. 43

44 x 0-3 Delta w Delta w 0 - Frequency [pu] Time [sec] Figure 3.5 (a). Frequency deviation 0.35 Delta P m 0.3 Delta P m Delta P Power [pu] Time [sec] Figure 3.5. Simulation results of figure 3.4 Figure 3.5(b). Power deviation. 44

45 Comparing between the responses of both the I term and the full PID controller, we can observe that the response of the PID controller is more satisfactory according to the optimized step response characteristics, including lower overshoot, less vibration, lower rise time and settling time and almost zero steadystate error AGC With Optimal Dispatch Of Generation (EDG) There are several factors that affect the power generation at minimum cost; these are efficiencies, fuel cost, and transmission losses and other many factors. Many types of programs were developed to find the optimal dispatch of generation of an interconnected power system [] [8]. The optimal dispatch of generation may be treated within the framework of as the third level. In direct digital control systems, the digital computer is included in the control loop which scans the unit generation and tie-line flows, the results are compared with the optimal settings that found from the solution of optimal dispatch programs. Now, if the actual settings are off from the optimal values, the computer generates the raise/lower pulses which sent to the individual units. With the development of control theory, several concepts are included in the AGC which go beyond the simple tie-line bias control. The fundamental approach is the use of more extended mathematical models. Other concepts of the modern control theory are being employed, such as state estimation and optimal control with linear regulator utilizing constant feedback gains. 45

46 Conclusions and further work. Load frequency control investigated in this project has recently come into question in operation of interconnected power networks. Frequency is a sensitive parameter which affects the system operation so it is controlled certainly. Therefore, power utilities consider the frequency and active power balance throughout their networks to sustain the interconnection. In interconnection between national/continental networks, providing the constant frequency between areas is a serious operational problem. Hence fast and no delay decision-making mechanism have to be installed in network control units namely the.. The load frequency control is achieved within tree levels, considering many issues from maintaining constant frequency and the minimization of losses through tie lines to the optimal dispatch of generation between units or even areas. 3. The simulation techniques are very useful in studying and predicting the response of control systems, giving the opportunity to optimize the response and so the behavior of the system under study. 4. The great importance of the PID controllers is recognized, considering the facilities it offers by the different combinations of its terms. 5. As a further work, study could be extended to consider methods of optimal design of the gains of the PID controllers, like considering the artificial intelligence methods or the fussy logic giving the opportunity to obtain an optimal response of the control systems. 6. The economic dispatch of generation plays a vital rule in the AGC, and this issue could be studied as an extension of this project, adding an additional dimension to the task of our project. 7. A larger and more complex control system could be considered by combining both and AVR systems together with the EDG system. 46

47 REFERENCES: []. Electric Machinery Fundamentals, By Stephen J. Chapman. 4 th Edition (005). []. Power System Analysis, by Hadi Saadat. nd Edition (00). [3]. PID Controllers, by K. J. Astrom and T. Hagglund (995). [4]. Modern Control Systems, by Richard C. Dorf and Robert H. Bishop. 9 th Edition (000). [5]. Demos of MATLAB program (version 7.6). [6]. Power Generation Operation and Control, by A.J. Wood and B.F. Wollenberg, John Wiley & Sons, New York, 984. [7]. Power System Stability and Control, by Kundur P, McGraw-Hill, NewYork 994. [8]. Electric Energy Systems Theory: An Introduction, By Olle I. Elgerd, University of Florida. 47